Peter Gaidarov

on the beauty of solving a maths problem

Peter is a student at Cambridge. His main interest is the science of mathematics; he started working hard on his maths skills in grade eight.

You are an acclaimed mathematician already. Can you tell us about your accomplishments?

Competitions in mathematics can be divided in two main types. The first ones are those that are timed (4 hours for instance) and with a fixed number of problems whose answers are known by the evaluation committee. They are very much like the work done in class, only the problems are more difficult.

The second type of competition is writing a research paper. In this case, a student works on a problem that has not been solved yet and there is no time limit for finding a solution. Usually, the work is done together with a mentor who is a more experienced mathematician. The whole process resembles the work on a scientific research project.

As a rule, it’s a rare case that a student is equally successful in both types of competitions. Fortunately, I am such a lucky exception to the rule. In the ‘short’ competitions I have had success in a Russian Maths Olympics and in a similar competition amongst the Balkan countries. But I am really in my element when I am writing a project. And my greatest achievements are with such written reports and projects, like my participation in the Summer School at the MIT Research Science Institute and the Intel ISEF, which are the European and the world’s largest competition for pre-college students.

What skills and competences are needed to be successful at these competitions?

The most important one is, of course, the ability to solve mathematical problems. I must admit that talent does have a role to play, but not a major one as most people believe. It is much more important to work hard.

In the short competitions it is crucial to be able to concentrate and to manage to do your best in a limited period of time.

When working on a project, on the other hand, the key competences needed are communication and presentation skills. During the preparation phase various types of approaches and styles of communication are practised (making a presentation, preparing a poster, elevator speeches are rehearsed) and a number of techniques are mastered with which to attract the audience’s attention. This to a great extent contradicts with the popular image of mathematicians as nerds who cannot hold a conversation.

What are the feelings that you experience when solving maths problems?

Sometimes, when an elegant solutions springs to mind, I get the feeling of beauty because of the solution I was able to come up with; and this beauty cannot be visualized or heard in any way, it is experienced on a different level. I suppose in every field, even if things are not visible to the laymen, experts can feel the beauty of a certain positive result.
Another feeling I experience often because of the magic of mathematics is the desire to learn more and more about a different subfield of knowledge. When I go deeper into a certain problem, questions arise one after another in a logical order and once you have found a solution to the most urgent one, then comes the next one, which might be even harder. This gradual advancing into a certain area is of particular interest for me.

Imagine you can solve all possible mathematical problems in the world? Which one would be of top priority for you?

I would give priority to those problems, which constitute a direct threat to human life and development, or to a group of people. Human life must be valued above all else.